Manipulating Surds (AQA GCSE Maths): Flashcards

Expressions containing irrational square roots that can't be simplified to fractions or whole numbers (e.g., $\sqrt{2}$, $\sqrt{3}$)

$\sqrt{a \times b}$

$b$

$\sqrt{a \div b}$

Cannot be simplified further

$a^2 + 2a\sqrt{b} + b$

$a^2 - b$

Multiply top and bottom by $\sqrt{b}$ to get $\frac{a\sqrt{b}}{b}$

Factor out perfect squares: $\sqrt{100 \times 3} = 10\sqrt{3}$

NOT equal to $\sqrt{a + b}$